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Science

A fully programmable 100-spin coherent Ising machine with all-to-all connections

Peter L. McMahon, Alireza Marandi, Yoshitaka Haribara, Ryan Hamerly, Carsten Langrock, Shuhei Tamate, Takahiro Inagaki, Hiroki Takesue, Shoko Utsunomiya, Kazuyuki Aihara, Robert L. Byer, M. M. Fejer, Hideo Mabuchi, Y. Yamamoto

Published Oct 21, 2016• 703 citations
Publisher

Abstract

Taking the pulse of optimization Finding the optimum solution of multiparameter or multifunctional problems is important across many disciplines, but it can be computationally intensive. Many such problems defined as computationally difficult can be mathematically mapped onto the so-called Ising problem, which looks at finding the minimum energy configuration for an array of coupled spins. Inagakiet al.and McMahonet al.show that an optical processing approach based on a network of coupled optical pulses in a ring fiber can be used to model and optimize large-scale Ising systems. Such a scalable architecture could help to optimize solutions to a wide range of complex problems. Science, this issue pp. 603 and 614

DOI
10.1126/science.aah5178

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Taking the pulse of optimization Finding the optimum solution of multiparameter or multifunctional problems is important across many disciplines, but it can be computationally intensive. Many such problems defined as computationally difficult can be mathematically mapped onto the so-called Ising problem, which looks at finding the minimum energy configuration for an array of coupled spins. Inagakiet al.and McMahonet al.show that an optical processing approach based on a network of coupled optical pulses in a ring fiber can be used to model and optimize large-scale Ising systems. Such a scalable architecture could help to optimize solutions to a wide range of complex problems. Science, this issue pp. 603 and 614
Combinatorial optimization problems are central to many challenges in logistics, finance, engineering, and the life sciences, yet they remain among the most computationally demanding. Many of these problems can be mapped onto the Ising model, in which binary spins interact through a network of couplings, and solutions correspond to low-energy, ideally ground-state, spin configurations. Photonic Ising machines have the potential to be fast and energy-efficient heuristic solvers of optimization problems by leveraging the low latency, high bandwidth, and inherent parallelism of optics. However, current photonic implementations remain limited in scalability, connectivity, reconfigurability, and time-to-solution, preventing their use in many practical applications. In this perspective, we examine the current landscape of photonic Ising machines, discuss the challenges and limitations of existing platforms, and identify the scientific and technological advances needed to realize large-scale systems. These developments could establish photonic Ising machines as useful hardware platforms for practical optimization.
Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.
The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.
Combinatorial optimization problems over large and complex systems have many applications in social networks, image processing, artificial intelligence, computational biology and a variety of other areas. Finding the optimized solution for such problems in general are usually in non-deterministic polynomial time (NP)-hard complexity class. Some NP-hard problems can be easily mapped to minimizing an Ising energy function. Here, we present an analog all-optical implementation of a coherent Ising machine (CIM) based on a network of injection-locked multicore fiber (MCF) lasers. The Zeeman terms and the mutual couplings appearing in the Ising Hamiltonians are implemented using spatial light modulators (SLMs). As a proof-of-principle, we demonstrate the use of optics to solve several Ising Hamiltonians for up to thirteen nodes. Overall, the average accuracy of the CIM to find the ground state energy was ~90% for 120 trials. The fundamental bottlenecks for the scalability and programmability of the presented CIM are discussed as well.
Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.